The pixelated Medipix detectors have been developed by the Medipix Collaboration to perform real-time imaging. The semiconducting chip is divided into 65536 pixels of $55\times 55\um^2$ for a total active area of nearly $2\cm^2$. Because of their sensitivity to all kinds of particles, sixteen Medipix2 detectors (ATLAS-MPX) have been placed in the ATLAS detector and its cavern to measure for the radiation produced by the head-on proton collisions produced at the LHC. At the next ATLAS upgrade, the ATLAS-MPX network will be extended to include the Timepix detectors, the latest version that allows one to measure the total energy deposited in the semiconductor.
To improve data analysis, a Geant4 simulation project of a Timepix detector was initiated by John Id\'arraga at the Université de Montréal. In the framework of the ATLAS experiment, this simulation could be used with Athena, the ATLAS analysis software, and the full ATLAS simulation.
Due to their repulsivity, the charge carriers created by an incoming particle in the pixelated detector are spread over the surrounding pixels causing a charge sharing effect. An effective model has been developed to reproduce this effect without resolving the charge drift's differential equation. This model and the \textit{time-over-threshold} mode of the Timepix have been included in the simulation to reproduce the tracks left by the striking particles. First, one had to individually calibrate each pixel of the device with $\Am$ and $\Ba$ sources. The simulation's validation has been performed with low energy protons and $\alpha$ particles delivered by the van de Graaff Tandem at the Laboratoire René-J.-A.-Lévesque of the Université de Montréal.